1. Technical Field
The present invention relates to a piezoelectric resonator element, a resonator gyro element, and the like, and more particularly, to a piezoelectric resonator element, a piezoelectric resonator, a piezoelectric oscillator, a resonator gyro element, and a resonator gyro sensor that are decreased in size and have improved frequency-temperature characteristics and an electronic apparatus using them.
2. Related Art
Generally, in a small-size information device such as a mobile computer, a hard disk drive or a mobile communication device such as a cellular phone, a piezoelectric device is widely used as a reference frequency source. In accordance with the progress of decrease in size of electronic apparatuses in which a piezoelectric device is mounted, a further decrease in the size of the piezoelectric device has been requested.
In JP-A-55-75326, a tuning fork type quartz crystal resonator is disclosed which is cut out in the range of 0° to −15° at the rotation of an electric axis (one of crystal axes) of quartz crystal. The frequency-temperature characteristics of the flexural resonator mode of the principal resonator of the quartz crystal resonator are enhanced by approaching and combining the resonance frequencies fF and fT of the flexural resonator mode and the torsional resonator mode that are excited in the tuning fork type crystal quartz resonator.
Generally, the frequency-temperature characteristics Δf/f of a quartz crystal resonator is represented by a polynomial with respect to temperature T. However, for practical use, the frequency-temperature characteristics are approximated as a cubic polynomial, and the first-order coefficient to the third-order coefficient are denoted by α, β, and γ. The frequency-temperature characteristics TfF of the flexural resonator mode are influenced by the torsional resonator mode and depend on the thickness h of a piezoelectric substrate. The thickness h is set such that the first-order coefficient α=0 for various cutting angles θ, and, additionally, the cutting angle θ and the thickness h for which the second-order coefficient β is zero are set from values acquired in advance through calculation. Accordingly, the frequency-temperature characteristics TfF depend only on the third-order coefficient γ, and it is disclosed that a quartz crystal resonator having satisfactory temperature characteristics is acquired.
In addition, in JP-A-2004-282230, a tuning fork type piezoelectric resonator is disclosed in which an expansion portion wider than a vibrating arm is disposed in each tip end portion of a plurality of vibrating arms that are parallel to one another. It has been written therein that the expansion portion has a bottomed hole, and a material having a specific gravity higher than that of a piezoelectric material is filled in the bottomed hole so as to serve as a spindle, whereby the miniaturization of the tuning fork type piezoelectric resonator is achieved.
Furthermore, in JP-A-2010-2430, a resonator gyro element is disclosed. The resonator gyro element includes: a base portion; one pair of detection vibrating arms that extend from the base portion to both sides in a linear shape; one pair of connecting arms extending from the base portion to both sides in directions perpendicular to the detection vibrating arms; and one pair of driving vibrating arms extending from the tip end portions of the connecting arms to both sides to be perpendicular to the tip end portions. In addition, two pairs of beams extending from the base portion along the detecting arms and one pair of support portions to which the beams extending in the same direction are connected are included in the same plane, and the support portions are configured to be arranged on the outer side of the detection vibrating arms in directions in which the detection vibrating arms extend and between the driving vibrating arms.
However, according to the tuning fork type piezoelectric resonator, which is disclosed in JP-A-55-75326, of which the frequency-temperature characteristics are improved by approaching and combining the frequencies of the flexural resonator mode and the torsional resonator mode, there is a problem in that it is difficult to decrease the size thereof.
In addition, according to the tuning fork type piezoelectric resonator disclosed in JP-A-2004-282230, although the size thereof can be decreased by forming the spindle portion in the tip end portion of the vibrating arm, the frequency-temperature characteristics have second-order characteristics, and there is a problem in the frequency stability.
Furthermore, according to the resonator gyro element disclosed in JP-A-2010-2430, there is a problem in that the sensitivity for the angular velocity changes in accordance with a change in the temperature.